The directional absorptivity of a gray surface varies with \(\theta\) as follows.

(a) What is the ratio of the normal absorptivity \(\alpha_{n}\) to the hemispherical emissivity of the surface?

(b) Consider a plate with these surface characteristics on both sides in earth orbit. If the solar flux incident on one side of the plate is \(q_{S}^{\prime \prime}=1368 \mathrm{~W} / \mathrm{m}^{2}\), what equilibrium temperature will the plate assume if it is oriented normal to the sun's rays? What temperature will it assume if it is oriented at \(75^{\circ}\) to the sun's rays?

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0.9 0 0.1 Che 0 = 60